Average Error: 0.2 → 0.5
Time: 1.3m
Precision: 64
Internal Precision: 576
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}} - 1\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}} - 1\]

  4. Final simplification0.5

    \[\leadsto \left(\sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}} - 1\]

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))